Purification of the concatenated Greenberger–Horne–Zeilinger state with linear optics

Logic qubit plays an important role in quantum computation. Recent research showed that logic qubit entanglement can be used in long-distance quantum communication. In this paper, we describe an entanglement purification protocol (EPP) for one type of logic qubit entanglement, named concatenated Greenberger–Horne–Zeilinger(C-GHZ) state. Not only the logic bit-flip and phase-flip errors in the C-GHZ state but also the single physical qubit bit-flip and phase-flip errors in the logic qubit can be purified. This EPP does not require the sophisticated controlled-not gate, but only requires some feasible linear optical elements, which is feasible in the current experimental condition.